Camach700 wrote:
EMPOWERgmatRichCany suggestion for testing the answer here?
Hi, Camach700,
YES - you can TEST THE ANSWERS here, but before you start doing that work, you have to hash out all of the information that the prompt gives you to work with. We're given a number of facts in this wordy prompt (and I'm going to summarize the information into my own words):
1) Bus A and Bus B are approaching each other while they each drive at the same constant speed. The buses are both driving the same route.
2) The buses meet at point P after driving for 2 hours each.
3) The following day the buses do the return trip at the same constant speed. One bus (Bus A) is delayed 24 minutes and the other (Bus B) leaves 36 minutes earlier.
4) The NEW meeting point is 24 miles from point P
We're asked for the distance between the two cities.
To start, the 24-minute delay for one bus (Bus A) and a 36-minute early-start for the second bus (Bus B) means that Bus B travels for 1 hour MORE than Bus A does. That 1-hour "head start" has to move the MEETING POINT 24 miles. You might assume that the busses were moving 24 miles/hour, but that would NOT be correct; keep in mind that BOTH Buses will still be moving when they meet (so that 24-mile difference still has to accommodate 2 moving busses)....
Let's start by TESTing one of the larger Answers....
Answer C: 96 miles.
IF... the two buses met after 2 hours of travel, then the 4 total hours of travel would have covered 96 miles and Point P is at the 48-mile 'mark.'
D = (R)(T)
96 miles = (R)(4 hours)
96/4 = 24 miles/hour = R
On the second day, Bus B has a head start, so it travels 24 miles before Bus A gets going. Thus, the two buses would then have to travel the remaining 96-24 = 72 total miles together at 24 miles/hour each. Each hour, the TOTAL distance traveled would be 48 miles.... 72/48 = 1.5 total hours of travel, so each bus would travel 1.5 hours.
In this situation, the buses meet after Bus A has traveled 1.5 hours at 24 miles/hour.... (1.5)(24) = 36 miles.... the 36-mile 'mark.' This is NOT 24 miles away from point P.... it's only 48 - 36 = 12 miles away. This is exactly HALF the distance that it needs to be.... so I'd look to DOUBLE the total distance...
Let's TEST Answer E: 192 miles
IF... the two buses met after 2 hours of travel, then the 4 total hours of travel would have covered 192 miles and Point P is at the 96-mile 'mark.'
D = (R)(T)
192 miles = (R)(4 hours)
192/4 = 48 miles/hour = R
On the second day, Bus B has a head start, so it travels 48 miles before Bus A gets going. Thus, the two buses would then have to travel the remaining 192 - 48 = 144 total miles together at 48 miles/hour each. Each hour, the TOTAL distance traveled would be 96 miles....144/96 = 1.5 total hours of travel, so each bus would travel 1.5 hours.
In this situation, the buses meet after Bus A has traveled 1.5 hours at 48 miles/hour.... (1.5)(48) = 72 miles.... the 72-mile 'mark.' This is 96 - 72 = 24 miles from Point P, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
_________________